Without being redundent and tell you this is what I think.
The latter situation you describe is usually the best course of action. Each of us interpets events diffrently. Ever play that game where you tell the first person "The red duck wears one magenta boot." and in the end it ends up "I saw your mom with a duck and a cowboy boot?" Let the players decide where to go with the game - just provide some guidance and a good starting point.
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